The Death Star only being damaged, resulting in its appearance in RotJ, does seem to be the most obvious solution. However, without a complete destruction of the battle station the end of ANH would be too confusing. The Rebels wouldn't be hanging around celebrating, they'd be getting the hell out of there. And what about Tarkin and all the other officers on the Death Star? How would it be made clear they died in the attack? Constructing a Vader/Palpatine conversation about repairing the damaged Death Star would aslo be much more difficult than referencing a *destroyed* Death Star.

There might be a way to pull it all together, but as you can see there would be much to overcome.